Mathematics Knowledge Answer

 

In working as an ASVAB tutor, I remind my student of the importance of memorizing various formulas for the shapes in geometry.  There are many geometry topics on the Mathematics Knowledge section of the ASVAB.  I remind students to be aware of the formulas for area, circumference, surface area, and volume.  Different shapes that can appear on the test include two-dimensional and three-dimensional shapes.  Examples include: squares, rectangles, triangles, circles, cubes, rectangular boxes, cylinders, spheres, etc.

Yesterday I presented a Mathematics Knowledge question.

The question is about the volume of a sphere.

The question is:

If the radius of a sphere is 1, what is the volume?

  1. 14
  2. 1762
  3. 28
  4. 56

In order to answer this question, you need to know the formula for the volume of a sphere.

This can be a challenging formula.

The volume of a sphere is V = 4/3 x pi x r3.

I tell my students that this is a time consuming formula.

If you multiply 4/3 x pi, the answer is 4.1762

If you use this formula V = 4.1762r3, you will find the exact answer in a quicker way.

To solve this problem, plug in 1 for the radius

V = 4.1762r3 = 4.1762 (1)3 = 4.1762(1) = 4.1762

To find the answer in a quicker way, you can use the simpler sphere formula.

This formula is V = 4r3.

This will not give an exact answer but an estimate.  The real answer will be a little bigger.

V = 4r3 = 4(1)3 = 4(1) = 4

4 is an estimate.  The real answer is 4.1762

If the answer choices are not that close, the estimate is a good way to save time on this problem.

Make sure you review all your formulas for the Mathematics Knowledge section of the test.